A learned linear solver converges only to the projection of the true solution operator onto the training-data function space, and richer polynomial training data can actually increase the finite-difference parameter bias.
Elliptic pde learning is provably data-efficient
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Interpretability and Generalization Bounds for Learning Spatial Physics
A learned linear solver converges only to the projection of the true solution operator onto the training-data function space, and richer polynomial training data can actually increase the finite-difference parameter bias.